math_expressions 1.1.1
math_expressions #
A library for parsing and evaluating mathematical expressions.
 Performs evaluations in real, vector, and interval contexts.
 Supports expression simplification and differentiation.
math_expressions is inspired by mathExpr for Java and distributed under the MIT license.
Features #
 Evaluation of expressions in various modes: Real, Vector and Interval.
 Parsing, simplification and differentiation of mathematical expressions.
 Supporting most basic math functions out of the box.
 Extensible through custom function definitions in code.
 Well documented and tested.
This package contains a very simple commandline interpreter for real numbers:
pub run math_expressions:interpreter
What's not working yet? #
 Some evaluations in vector and interval space (especially functions).
 Ndimensional vectors. Curently no more than four dimensions are supported.
 The parser only works for real numbers.
 Complex numbers.
Suggestions and pull requests are always welcome!
Usage #
Below are two basic examples of how to use this library. There also is some additional example code available.
1. Expression creation and evaluation #
This example shows how to evaluate
for
Build the expression
You can either create an mathematical expression programmatically or parse a string.
 Create the expression programmatically:
Variable x = new Variable('x'), y = new Variable('y');
Power xSquare = new Power(x, 2);
Cos yCos = new Cos(y);
Number three = new Number(3.0);
Expression exp = (xSquare + yCos) / three;
 Create the expression via the parser:
Parser p = new Parser();
Expression exp = p.parse("(x^2 + cos(y)) / 3");
Evaluate the expression
 Bind variables and evaluate the expression as real number:
// Bind variables:
ContextModel cm = new ContextModel();
cm.bindVariable(x, new Number(2.0));
cm.bindVariable(y, new Number(Math.PI));
// Evaluate expression:
double eval = exp.evaluate(EvaluationType.REAL, cm);
print(eval) // = 1.0
2. Expression simplification and differentiation #
This example shows how to simplify and differentiate
 Expressions can be simplified and differentiated with respect to a given variable:
Expression exp = p.parse("x*1  (5)");
print(exp); // = ((x * 1.0)  (5.0))
print(exp.simplify()); // = (x + 5.0)
Expression expDerived = exp.derive('x');
print(expDerived); // = (((x * 0.0) + (1.0 * 1.0))  (0.0))
print(expDerived.simplify()); // = 1.0
Alternatives #
Here are some other Dart libraries that implement similar functionality to math_expression: parsing and evaluating mathematical expressions.
 expressions: an elegant and small library to parse and evaluate simple expressions.
 function_tree: a library for parsing, evaluating and plotting single and multivariables numerical functions.
To the author's knowledge math_expressions is currently the only library supporting interval arithmetics.
1.1.1  20190416 #
 Package health and maintenance cleanups
1.1.0  20190416 #
 Drop support for Dart SDK versions below 2.0.0
 Add arcsin, arccos, arctan functions
 Fix floor and ceil functions
 Update examples and documentation
 Switch to pendantic analysis options
1.0.0  20180811 #
 Add support for Dart 2.0
 Drop support for Dart SDK versions below 1.24.0
 Depend on
vector_math
2.0.0 or newer
0.4.0  20180810 #
 Last release to only support Dart 1.x
 Prepare for Dart 2.0
 Enable strong mode
 Analyzer and linter fixes
 Drop support for Dart SDK versions below 1.21.0
0.3.0  20160709 #
 Rename
Point3D
toPoint3
Point3
now is a subtype ofVector3
 Add mod (%) operator and ceil, floor functions
 Fixing a few missed chain rules in
derive
0.2.0+1  20151230 #
 Depend on
vector_math
1.4.4 or greater
0.2.0  20151119 #
 Add support for basic vector operations
 Switch to using
test
instead ofunittest
package  Warning: Depends on git version of
vector_math
as latest pub release is severely outdated
0.1.0  20140719 #
 Add absolute value function (by markhats)
 Add sign function
 Improve test coverage
 Adapt string representation of unary minus to standard syntax
0.0.9  20140330 #
 To create exponentials, use
e(x)
ore^x
. Consequently, removed support forexp(x)
.  Improve test coverage
 Update dependencies
0.0.8  20131210 #
 Bring back standard syntax for unary minus:
5
works now. (by markhats)  Add parser support for
e^x
additional toexp(x)
. (by markhats)
0.0.7  20131109 #
 Introduce nested context/naming scopes
 Improve vector evaluation
 Add some missing methods
 Improve test coverage (custom and composite functions)
 Remove boilerplate code
0.0.6  20131107 #
 Add compose operator for functions:
Use&
to conveniently create a CompositeFunction from two existing functions:expr = f & g;
 Improve documentation and dartdoc generation
0.0.5  20131106 #
 Minor code cleanup
 Prepare for Dart 1.0
0.0.4  20131011 #
 Fix handling of operator associativity
 Add support for default functions to parser
 Add support for unary minus to parser:
Input with underscore. Instead of2*5
use2*_5
.
0.0.3  20131009 #
 Add cli evaluator to examples
 Improve test coverage
 Fix bug in differentiation of Sin and Cos
 Remove support of unary minus in Parser
0.0.2  20131007 #
 Improve test coverage
 Improve documentation
 Fix bug in simplification of Minus
 Fix bug in simplification of Times
 Implement evaluation of nth root
0.0.1+1  20131006 #
 Improve documentation and examples
0.0.1  20131004 #
 Initial release of standalone version
import 'dart:math' as math;
import 'package:math_expressions/math_expressions.dart';
/**
* This file contains three examples:
*  Example 1: Expression creation and evaluation
* (through the Parser and programmatically)
*  Example 2: Expression simplification and differentiation
*  Example 3: Custom function definition and use
*/
void main() {
_expression_creation_and_evaluation();
_expression_simplification_and_differentiation();
_custom_function_definition_and_use();
}
/**
* Example 1: Expression creation and evaluation
*
* How to create an expression (a) via the Parser, (b) programmatically,
* and how to evaluate an expression given a context.
*/
void _expression_creation_and_evaluation() {
print('\nExample 1: Expression creation and evaluation\n');
// You can either create an mathematical expression programmatically or parse
// a string.
// (1a) Parse expression:
Parser p = new Parser();
Expression exp = p.parse('(x^2 + cos(y)) / 3');
// (1b) Build expression: (x^2 + cos(y)) / 3
Variable x = new Variable('x'), y = new Variable('y');
Power xSquare = new Power(x, 2);
Cos yCos = new Cos(y);
Number three = new Number(3.0);
exp = (xSquare + yCos) / three;
// Bind variables and evaluate the expression as real number.
// (2) Bind variables:
ContextModel cm = new ContextModel()
..bindVariable(x, new Number(2.0))
..bindVariable(y, new Number(math.pi));
// (3) Evaluate expression:
double eval = exp.evaluate(EvaluationType.REAL, cm);
print('Expression: $exp');
print('Evaluated expression: $eval\n (with context: $cm)'); // = 1
}
/**
* Example 2: Expression simplification and differentiation
*
* How to simplify an expression, and how to differentiate it with respect
* to a given variable.
*/
void _expression_simplification_and_differentiation() {
print('\nExample 2: Expression simplification and differentiation\n');
// (1) Parse expression:
Parser p = new Parser();
Expression exp = p.parse('x*1  (5)');
// (2) Simplify expression:
print('Expression: $exp'); // = ((x * 1.0)  (5.0))
print('Simplified expression: ${exp.simplify()}\n'); // = (x + 5.0)
// (2) Differentiate expression with respect to variable 'x':
Expression expDerived = exp.derive('x');
print(
'Differentiated expression: $expDerived'); // = (((x * 0.0) + (1.0 * 1.0))  (0.0))
print(
'Simplified differentiated expression: ${expDerived.simplify()}'); // = 1.0
}
/**
* Example 3: Custom function definition and use
*
* How to create an arbitrary custom function expression and evaluate it.
*/
void _custom_function_definition_and_use() {
print('\nExample 3: Custom function definition and use\n');
// (1) Create and evaluate custom function: DOUBLEUP (R > R)
ContextModel cm = ContextModel();
Variable x = Variable('x');
CustomFunction doubleup = CustomFunction('doubleup', [x], x * new Number(2));
cm.bindVariable(x, Number(0.5));
print('$doubleup = ${doubleup.expression}');
print(
'doubleup(${cm.getExpression('x')}) = ${doubleup.evaluate(EvaluationType.REAL, cm)}\n');
// (1) Create and evaluate custom function: LEFTSHIFT (R² > R)
// Shifting to the left makes the number larger, effectively multiplying the
// number by pow(2, shiftIndex). Custom implementation of x << i.
Variable shiftIndex = Variable('i');
CustomFunction leftshift = new CustomFunction(
'leftshift', [x, shiftIndex], x * new Power(2, shiftIndex));
cm.bindVariable(x, Number(250));
cm.bindVariable(shiftIndex, Number(8));
print('$leftshift = ${leftshift.expression}');
print(
'leftshift(${cm.getExpression('x')}, ${cm.getExpression('i')}) = ${leftshift.evaluate(EvaluationType.REAL, cm)}');
}
Use this package as a library
1. Depend on it
Add this to your package's pubspec.yaml file:
dependencies:
math_expressions: ^1.1.1
2. Install it
You can install packages from the command line:
with pub:
$ pub get
with Flutter:
$ flutter pub get
Alternatively, your editor might support pub get
or flutter pub get
.
Check the docs for your editor to learn more.
3. Import it
Now in your Dart code, you can use:
import 'package:math_expressions/math_expressions.dart';
Popularity:
Describes how popular the package is relative to other packages.
[more]

91

Health:
Code health derived from static analysis.
[more]

75

Maintenance:
Reflects how tidy and uptodate the package is.
[more]

100

Overall:
Weighted score of the above.
[more]

88

We analyzed this package on Feb 27, 2020, and provided a score, details, and suggestions below. Analysis was completed with status completed using:
 Dart: 2.7.1
 pana: 0.13.5
Health suggestions
Fix lib/src/functions.dart
. (25 points)
Analysis of lib/src/functions.dart
reported 76 hints, including:
line 24 col 46: Unnecessary new keyword.
line 98 col 13: Unnecessary new keyword.
line 104 col 12: Unnecessary new keyword.
line 113 col 12: Unnecessary new keyword.
line 173 col 11: Unnecessary new keyword.
Fix lib/src/parser.dart
. (25 points)
Analysis of lib/src/parser.dart
reported 62 hints, including:
line 16 col 20: Unnecessary new keyword.
line 24 col 13: Unnecessary new keyword.
line 35 col 22: Unnecessary new keyword.
line 38 col 22: Unnecessary new keyword.
line 74 col 22: Unnecessary new keyword.
Fix lib/src/expression.dart
. (24.10 points)
Analysis of lib/src/expression.dart
reported 55 hints, including:
line 32 col 44: Unnecessary new keyword.
line 35 col 44: Unnecessary new keyword.
line 38 col 44: Unnecessary new keyword.
line 41 col 44: Unnecessary new keyword.
line 44 col 44: Unnecessary new keyword.
Fix additional 3 files with analysis or formatting issues. (23.40 points)
Additional issues in the following files:
lib/src/algebra.dart
(36 hints)lib/src/evaluator.dart
(8 hints)bin/interpreter.dart
(6 hints)
Dependencies
Package  Constraint  Resolved  Available 

Direct dependencies  
Dart SDK  >=2.0.0 <3.0.0  
vector_math  ^2.0.0  2.0.8  
Dev dependencies  
pedantic  ^1.4.0  
test  ^1.3.0 